Nonlinear Vibration and Dynamic Reliability of Membrane Under Non-Gaussian Excitation: Theory and Experiment

The structural reliability analysis of flexible engineering structures considering the geometrical nonlinearity remains a challenge, especially in non-Gaussian excitations such as typhoons. In this study, the theoretical model of nonlinear random vibration and reliability assessment of hyperbolic paraboloid membrane structures is proposed. First, the random nonlinear vibration governing equations are derived and analytically solved, considering the geometric nonlinear stiffness and nonlinear motion-induced aerodynamic force. Consequently, the statistical moments of the steady-state displacement response are obtained. Second, the structural reliability is accurately determined by using an enhanced high-order moment method. Third, the developed theoretical model is validated by a series of wind tunnel tests. The results demonstrate that the proposed method has fairly high accuracy and efficiency for structural high-order moments estimation and reliability assessment. This study demonstrates that geometric nonlinearity and aerodynamic forces have counteracting effects on structural reliability, with the former providing substantial enhancement and the latter a moderate reduction. A reduced wind velocity of 1.2 and a rise-to-span ratio of 1/10 are identified as critical for design. The presented framework successfully captures essential non-Gaussian features, offering a validated analytical tool for assessing the typhoon resilience of flexible membrane structures.